Related papers: Phase transition behavior in a cellular automaton …
Thermal activation and macroscopic quantum tunneling in current-biased discrete Josephson transmission lines are studied theoretically. The degrees of freedom under consideration are the phases across the junctions which are coupled to each…
Cellular automata have turned out to be important tools for the simulation of traffic flow. They are designed for an efficient impletmentation on the computer, but hard to treat analytically. Here we discuss several approaches for an…
Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining…
The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional…
The development of neuromorphic systems based on memristive elements - resistors with memory - requires a fundamental understanding of their collective dynamics when organized in networks. Here, we study an experimentally inspired model of…
Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss…
We investigate dissipative phase transitions in an open central spin system. In our model the central spin interacts coherently with the surrounding many-particle spin environment and is subject to coherent driving and dissipation. We…
Predicting selfish behavior in public environments by considering Nash equilibria is a central concept of game theory. For the dynamic traffic assignment problem modeled by a flow over time game, in which every particle tries to reach its…
The Biham-Middleton-Levine (BML) traffic model, a cellular automaton with east-bound and north-bound cars moving by turns on a square lattice, has been an underpinning model in the study of collective behaviour by cars, pedestrians and even…
We develop a discrete Boltzmann-type model that uses dynamics in phase space to describe the behavior of traffic flows. Firstly, we model the traffic flow at mesoscopic scale using dynamics in phase space, which is considered as an…
In neural circuits, statistical connectivity rules strongly depend on neuronal type. Here we study dynamics of neural networks with cell-type specific connectivity by extending the dynamic mean field method, and find that these networks…
Phase transitions and critical behavior of driven systems are reviewed. Models exhibiting phase transitions, spontaneous symmetry breaking, phase separation and coarsening processes in d=1 dimension are discussed.
We propose a traffic flow model in which the vehicles are filed from their maximal velocities, the fast cars run with $Vmax{1}$, whereas the slow ones run with $Vmax{2}$. Using new overtaking rules which deals with deterministic NaSch…
We study the fluctuations of time-additive random observables in the stochastic dynamics of a system of $N$ non-interacting Ising spins. We mainly consider the case of all-to-all dynamics where transitions are possible between any two spin…
We investigate the physical properties of steady flows in a holographic first-order phase transition model, extending from the thermodynamics at equilibrium to the real-time dynamics far from equilibrium. Through spinodal decomposition or…
We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g. cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion…
A bottleneck simulation of road traffic on a loop, using the deterministic cellular automata (CA) Nagel-Schreckenberg model with zero dawdling probability, reveals three types of stationary wave solutions. They consist of i) two shock…
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics…
We investigate two models for traffic flow with modified acceleration ('slow-to-start') rules. Even in the simplest case $v_{max}=1$ these rules break the 'particle-hole` symmetry of the model. We determine the fundamental diagram…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…